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Revista Colombiana de Estadística

Print version ISSN 0120-1751

Rev.Colomb.Estad. vol.43 no.2 Bogotá July/Dec. 2020  Epub Dec 05, 2020

https://doi.org/10.15446/rce.v43n2.81979 

Original articles of research

On Predictive Distribution of K-Inflated Poisson Models with and Without Additional Information

Acerca de la distribución predicitiva de modelos Poisson K -inflados

Abdolnasser Sadeghkhani1  a 

S. Ejaz Ahmed2  b 

1Departmento de Estadística, Instituto Tecnológico Autónomo de México, Ciudad de México, México

2Department of Mathematics and Statistics, Brock University, Ontario, Canada


Abstract

This paper addresses different approaches in finding the Bayesian predictive distribution of a random variable from a Poisson model that can handle count data with an inflated value of K Є ℕ, known as the KIP model. We explore how we can use other source of additional information to find such an estimator. More specifically, we find a Bayesian estimator of future density of random variable Y 1 , based on observable X 1 from the K1IP(p1 , λ 1 ) model, with and without assuming that there exists another random variable X 2 , from the K2IP(p 2 , λ 2 ) model, independent of X1, provided λ 1 ≥ λ 2, and compare their performance using simulation method.

Key words: KIP model; Bayesian statistics; Bayesian predictive distribution; Simulation

Resumen

Este artículo presenta diferentes enfoques para buscar la distribución bayesiana predictiva de una variable aleatoria con un valor inflado K Є ℕ conocido como el modelo KIP. Se explora como usar una fuente de información adicional para encontrar el estimador. Específicamente, se busca un estimador Bayesiano de la densidad futura de una variable aleatoria Y 1 , basada en una variable observable X 1 a partir del modelo K1IP(p 1, λ 1), con y sin el supuesto de que existe otra variable aleatoria X 2 del modelo K2IP(p2, λ2), independiente de X 1 , si λ1 λ2, y se compara su desempeño usando un método de simulación.

Palabras clave: Modelo KIP; Estadísticas bayesianas; Distribución predictiva bayesiana; Simulación

Full text available only in PDF format.

Acknowledgements

Abdolnasser Sadeghkhani acknowledges the ITAM and Asociación Mexicana de Cultura, A.C. for supporting this paper. S. Ejaz Ahmed acknowledges the Natural Sciences and the Engineering Research Council of Canada, and the Ontario Centre of Excellence for supporting this research.

The authors are grateful to the editor and the anonymous reviewers for their valuable comments and helpful suggestions.

References

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Received: September 2019; Accepted: April 2020

aPh.D. E-mail: nasser@itam.mx

bPh.D. E-mail: sahmed5@brocku.ca

Creative Commons License This is an open-access article distributed under the terms of the Creative Commons Attribution License